graphs and coordinates

Question 1

how to find a mid point

Answer 1

[(x1+x2)/2 , (y1+y2)/2]

Question 2

how to find gradient

Answer 2

m = change in y/change in x

Question 3

if line 1 and line 2 are percpenticular to each other then

Answer 3

m1= -1/m2

Question 4

equation of line

Answer 4

y-y1 = m(x-x1)

Question 5

discriminate

Answer 5

b^2 - 4ac

Question 6

b^2 - 4ac>0

Answer 6

2 roots

Question 7

b^2 - 4ac=0

Answer 7

1 repeated root

Question 8

b^2 - 4ac<0

Answer 8

no real roots

Question 9

eqaution of cirlce

Answer 9

(x-a)^2 + (y-b)^2 =r^2
where centre is (a,b) and raduis is r

Question 10

sine graph when x=0

Answer 10

y=0

Question 11

cosine graph when x=0

Answer 11

y=1

Question 12

tangent graph when x=0

Answer 12

y=0

Question 13

tranformation f(x) +a

Answer 13

(0)
(a)

Question 14

tranformation af(x)

Answer 14

stretch in y direction by scale factor a

Question 15

tranformation f(x+a)

Answer 15

(-a)
(0)

Question 16

tranformation f(ax)

Answer 16

strech in x-direction by scale factor 1/a

Question 17

tranformation -f(x)

Answer 17

reflection in x-axis (flip it)

Question 18

tramformation f(-x)

Answer 18

reflection in y-axis (flip it)

Question 19

tranformation |f(x)|

Answer 19

anything below x axis goes up

Question 20

trafnmormation f(|x|)

Answer 20

anything to right of y-axis goes left

Question 21

how to work out tranformations

Answer 21

rearrange so everything outside bracket on y side then everything acts the opposite as expected